1. Field of the invention
The present invention generally relates to a filter circuit. More specifically, the present invention relates to a filter circuit including a first integrator to which a first input and a fed-back input are inputted, and a second integrator to which an output of the first integrator and a fed-back input are inputted.
2. Description of the Prior Art
In reference to FIG. 17, a conventional filter circuit 1 includes an output terminal 3 from which a signal obtained through a filtering process of a signal inputted from one of input terminals 2a and 2b is outputted. On the assumption that inputs from the input terminals 2a and 2b are V.sub.1 and V.sub.2, respectively, and an output of the output terminal 3 is V.sub.4, and a mutual conductance of a differential amplifier 4a is g.sub.m1, the output V.sub.4 is representative by the following equation 1. In addition, at a stage succeeding to the differential amplifier 4a, a buffer 5a is arranged. ##EQU1##
Furthermore, in view of the above described equation 1, a resonance frequency .omega..sub.0 can be represented by the following equation 2. ##EQU2##
Furthermore, in FIG. 18, another conventional filter circuit 1 is shown. The filter circuit 1 shown in FIG. 18 is a filter in which a differential amplifier 4b having a mutual conductance of g.sub.m2 and a buffer 5b are inserted between the input terminal 2a and the differential amplifier 4a of the filter circuit 1 shown in FIG. 17. An output of the buffer 5a is fed-back to the differential amplifier 4b; and an input terminal 2c is connected to a connection point of the differential amplifier 4b and the buffer 5b via a capacitor C.sub.2. In this case, when an input from the input terminal 2c is V.sub.3, the output V.sub.4 can be represented by the following equation 3: ##EQU3##
In addition, a resonance frequency .omega..sub.0 and a quality factor Q are represented by the following equations 4 and 5, respectively. ##EQU4##
In the filter circuit 1 shown in FIG. 17, in order to make the resonance frequency low, as seen from the equation 2, it is necessary to make the mutual conductance g.sub.m1 small and a capacity of the capacitor C.sub.1 large. However, if the mutual conductance g.sub.mi is made small, it is necessary to operate a transistor included in the differential amplifier 4a in a region where a current amount of the transistor is small, and therefore, a frequency characteristic of the transistor becomes bad. Consequently, it becomes difficult to operate the transistor in a region where an S/N is large. Furthermore, if the capacity of the capacitor C.sub.1 is made large, a chip area of an integrated circuit becomes large. Accordingly, it was difficult to set the resonance frequency low in the integrated circuit. Such a problem also occurs in the filter circuit 1 shown in FIG. 18.